标题： 一次性的变量比率匹配与精细平衡 显示英文标题

标题： One-shot variable-ratio matching with fine balance

摘要： 变量比例匹配是设计观察性研究以模拟目标随机对照试验（RCT）的灵活替代方法，它替代了传统的$1$-to-$k$匹配。 为了实现精细平衡——即匹配处理组和对照组，使其在选定协变量上的边缘分布相同——传统方法通常根据估计的整个数量将数据分成层次，然后在每个层次内进行一系列$1$-to-$k$匹配，其中$k$由层次特定的整个数量确定。 这种“分而治之”策略有显著的局限性：(1) 精细平衡通常不在最终合并样本中成立，(2) 可能丢弃比必要更多的对照组。 为了解决这些限制，我们提出了一种一次性变量比例匹配算法。 我们的方法在匹配样本中对选定协变量产生精确的精细平衡，模仿了一个假设的 RCT，其中单位首先被分组到不同大小的集合中，每个集合中一个单位被分配到处理组，其他单位被分配到对照组。 此外，与“分而治之”方法相比，我们的方法在许多协变量上实现了可比或更优的平衡，并保留了更多的对照组在最终匹配设计中。 我们通过模拟和使用一个研究危重患者右心导管插入术对死亡率影响的数据集来展示所提出设计的优势。 该算法在 R 包 match2C 中实现。 显示英文摘要

摘要： Variable-ratio matching is a flexible alternative to conventional $1$-to-$k$ matching for designing observational studies that emulate a target randomized controlled trial (RCT). To achieve fine balance -- that is, matching treated and control groups to have the same marginal distribution on selected covariates -- conventional approaches typically partition the data into strata based on estimated entire numbers and then perform a series of $1$-to-$k$ matches within each stratum, with $k$ determined by the stratum-specific entire number. This ``divide-and-conquer" strategy has notable limitations: (1) fine balance typically does not hold in the final pooled sample, and (2) more controls may be discarded than necessary. To address these limitations, we propose a one-shot variable-ratio matching algorithm. Our method produces designs with exact fine balance on selected covariates in the matched sample, mimicking a hypothetical RCT where units are first grouped into sets of different sizes and one unit within each set is assigned to treatment while others to control. Moreover, our method achieves comparable or superior balance across many covariates and retains more controls in the final matched design, compared to the ``divide-and-conquer" approach. We demonstrate the advantages of the proposed design over the conventional approach via simulations and using a dataset studying the effect of right heart catheterization on mortality among critically ill patients. The algorithm is implemented in the R package match2C.